A greedy randomized adaptive search procedure (GRASP) is a heuristic method that has shown to be very powerful in solving combinatorial problems. In this paper we apply GRASP to solve the transmission network expansion problem. This procedure is an expert iterative sampling technique that has two phases for each iteration. The first, construction phase, finds a feasible solution for the problem. The second phase, a local search, seeks for improvements on construction phase solution by a local search. The best solution over all GRASP iterations is chosen as the result